Sudanese demonstrators stand in front of the burning German embassy in Khartoum after Friday prayers on Sept. 14, 2012. The demonstrators broke into the U.S. and German embassy compounds and raised Islamic flags in state-backed protests against a film that insults the Prophet Mohammad, witnesses say

Is there anything the U.S. can do to stop the wave of often violent demonstrations across the Muslim world this week targeting its embassies and those of its allies? The short answer is no; it will have to ride out the rage stoked by opportunists in Muslim capitals looking to profit politically from genuine popular outrage at a film insulting the Prophet Muhammad — and hope that no more diplomats or protesters are killed, thereby further escalating the confrontation.

Friday saw protests in countries as far-flung as Sri Lanka, Nigeria and the Maldives, as well as deadly confrontations in Tunis, where three people were killed after the U.S. embassy compound was breached, and in Sudan’s capital, Khartoum, where one was killed after a similar breach. But Friday was always going to be a very bad day; as the Muslim day of prayer, it usually marks the zenith of any cycle of pan-Islamic protest, brings the global Muslim ummah together in mosques and affirms the bonds of a community of faith and submission to the God of Abraham. The Friday jummah prayer service symbolically reaffirms the community of the faithful, which can be used to remind them of the notion that an attack on Muslims anywhere, or on the symbols of their faith, should be felt as an attack on Muslims everywhere. Fridays, then, have in recent years always marked a high point in protests, whether against the invasion of Iraq, the abuse of detainees at Abu Ghraib prison, Israel’s bombing of Gaza or the desecration of the Koran by U.S. soldiers in Afghanistan or an obscure preacher in Florida. And, as in those previous rounds of protest, it’s a fairly safe bet that the outrage over the Innocence of Muslims film will eventually abate — although the death of protesters creates new grievances that can sustain the issue.

But White House press secretary Jay Carney may have been overreaching when he insisted on Friday that the protests arose “in response not to United States policy, not to the Administration, not the American people [but] in response to a video, a film that we have judged to be reprehensible and disgusting. That in no way justifies any violent reaction to it, but this is in no way a case of protests directed towards the United States writ large or at U.S. policies.”

It’s never that simple.

The reason a piece of “evidence” of American animus to Islam — the desecration of a Koran, say, or the dissemination of a video painting a grotesque caricature of the Prophet Muhammad — ignites rage toward U.S. institutions in so many Muslims is the way those Muslims have viewed and experienced U.S. policy. Direct insults of Islam such as those contained in the offending movie are such a powerful tool in the hands of those who would agitate against U.S. involvement in the Middle East — and against those in the Arab world who would work with Washington — because they function as a kind of narrative “gotcha!” motive that ties together all of the Arab world’s many grievances with the U.S. Egregious insults like the Innocence of Muslims film would not be so easily translated into rage at U.S. power were it not for the simmering long-term rage at Washington over its invasions of Muslim countries, its support for Israeli governments and Arab despots, its drone strikes and more.

Deep anger at U.S. foreign policy is the extended preexisting condition that geopolitical Obamacare has failed to significantly alter; the outrage at an offensive film is the opportunistic virus that, when combined with the preexisting condition, creates a crisis. Instances of American Islam-bashing are used to prove that the policies and actions of the U.S. that most anger ordinary Arabs are not simply discrete foreign policy choices driven by self-interest and other agendas but rather expressions of a deeper animus toward Islam itself — a proof that functions as a chemical catalyst that can bring residual anger to a boil.

Yes, it’s always manipulated by cynical opportunists driven by narrow political agendas, but the outrage itself is real, and it’s hardly confined to a movie. Without the pre-existing anger, in fact, the film would be like a detonator without dynamite. Only the combination of the two creates the explosion.

So in that sense, President Obama’s Republican critics are not wrong in suggesting that this week’s upsurge in protests represents, at least in part, a response to the Administration’s handling of the Middle East or even to what vice-presidential candidate Paul Ryan on Friday called “mixed signals” from the White House. But where Ryan and those echoing him are wrong — egregiously, spectacularly wrong — is in suggesting that the protests are a response to a retreat from “moral clarity and firmness of purpose,” watchwords of the Bush era. On the contrary, the Muslim world was up in arms against the U.S. on a sustained basis for most of the Bush presidency, precisely because of its wars in Iraq and Afghanistan, its unconditional backing of Israel as it pummeled Palestinians and the obvious hypocrisy of a policy of proclaiming democracy and freedom while coddling friendly despots. If the Arab world is angry at the “mixed messages” coming from the Obama Administration, that’s because the President in Cairo in 2009 had promised a break from Bush-era policies yet failed on many fronts to deliver it. It’s not the changes Obama’s made since the Bush era that drive Arab anger; it’s his Administration’s many continuities with Bush-era policies in the Middle East. Ryan demands that Obama show “American leadership” by marching even more closely in lockstep with Israeli Prime Minister Benjamin Netanyahu. That’s going to calm the crowds gathered in front of U.S. embassies in the Arab world?

Thoughtful foreign policy wonks from hawkish heavy hitter Robert Kagan, a key Bush Administration adviser during the Iraq war, to liberal experts in Arab politics like the Carnegie Endowment’s Nathan Brown concur in supporting a measured response that recognizes the political and social crises under way in the Arab world while seeking engagement with the emergent Islamist governments in order to push them in a more pragmatic direction.

The Muslim Brotherhood in Egypt appears to have tried to signal, however clumsily, that it too seeks engagement and a new relationship with Western powers. But it can’t ignore the stream of anger unleashed by the broadcasting on Salafist TV networks of clips from a crude video provocation. That’s why it has called on its followers to protest the film but to do so peacefully at their local mosques. In other words, not at the U.S. embassy. Something tells me that such roundabout efforts to calm the situation by encouraging but also limiting protest — as two-sided as they may seem to an American media audience — may offer the best hope of changing the dynamic. Events over the past week in Libya, Egypt, Tunisia and Yemen are a reminder that the region, and Washington’s relationship with it, has entered uncharted territory over the past two years.

Neither bromides about “moral clarity” nor evasions of the enduring contradictions and ambiguities in U.S. policy offer much guidance. As the Arab world changes, it asks new questions of itself and also of the major superpower in its midst. That conversation, which will be anything but comfortable, is only just beginning.

Tony Karon is a senior editor at TIME, where he has covered international conflicts in the Middle East, Asia, and the Balkans since 1997. A native of South Africa, he now resides with his family in Brooklyn, New York.